Ilya Khayutin, Mathematics
About
I am a Veblen Research Instructor at Princeton University and the Institute for Advanced Study since 2016. Before that I was a PhD student at the Einstein Institute of Mathematics at the Hebrew University of Jerusalem under the guidance of Prof. Elon Lindenstrauss.
Research
I work in number theory and homogeneous dynamics. My research revolves around equidistribution of arithmetic objects. This is a broad subject that requires a synthesis of ideas from different fields.
In a pursuit to understand equidistribution questions I am studying measure rigidity, arithmetic invariant theory, relative trace formulae and their geometric expansion, sieve methods in multiplicative number theory, subconvexity and large deviations estimates.
Teaching
In Fall 2018 I am teaching an advanced class about Ratner’s theorems and their applications in number theory.
Papers

Closed Geodesics on Products of Modular Curves, Ilya Khayutin, 2019, In preparation, tentative abstract

Nonvanishing of Class Group functions for Number Fields with a Small Regulator, Ilya Khayutin, 2019, preprint

Equidistribution on KugaSato Varieties of Torsion Points on CM Elliptic Curves, Ilya Khayutin, 2018, Submitted, arxiv

Joint Equidistribution of CM Points, Ilya Khayutin, 2017, Annals of Math., arxiv
Videos: 15min talk, 1hr talk 
Arithmetic of Double Torus Quotients and the Distribution of Periodic Torus Orbits, Ilya Khayutin, 2015, Accepted at Duke Math J., pending final revision, arxiv

Large Deviations and Effective Equidistribution, Ilya Khayutin, 2015, Int. Math. Res. Not., arxiv

Communication with Unobservable Constraints, Ilya Khayutin, 2007, Master’s Thesis, Manuscript
Contact
email: last name@princeton.edu
Fine Hall 509,
Princeton University.
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Princeton, NJ 08544
Fuld Hall 118,
Institute for Advanced Study.
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